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Father wants to file HoH, and claim one child.  Mother wants to file single, and claim 1 child, and also get the EIC from the 3rd child that she is custodial parent of, but child's father claims as dependent.

Doing the numbers, when Father claims 2 children (can't claim 3rd, stepson, child's father claims him) with Child Tax credit, dependency, and EIC, refund is around 500. Mother with no children is also around 500.

 Doing the numbers the way in question, father owes approx $1500, but mother refund is around $6000

Is it possible to each claim one of the other two children, one each, to take advantage of the much higher EIC with mother's lower income?